IMAGE PROCESSING

Table Tennis Ball Detection-MATLAB CODE:

Using the concept of roundness to detect a circular object, the table tennis ball in mid air or in palm is detected.

FLOW CHART:

1. Read input image

· Read a RGB image with ball in mid air or ball in palm.

MATLAB CODE:

%Read the input image

Img=imread(Filename);

axes('Position',[0 .1 .74 .8],'xtick',[],'ytick',[]);

imshow(Img);title('Original Image');

2. Image Pre-processing

· Convert the RGB image to grayscale image.

· Apply median filter

· Adjust the brightness and contrast of the image using ‘imadjust’ function.

MATLAB CODE:

I=rgb2gray(Img); % Converting RGB Image to

% Gray Scale Image

I=im2double(I); % Converting Gray scale Image

% to Double type

J = medfilt2(I,[3 3]); % Median Filter ,

% 3x3 Convolution

% on Image

I2 = imadjust(J); % Improve to quality of Image

% and adjusting

% contrast and brightness values

3. Threshold the image

· The pixel value greater than the threshold value is converted to one else zero.

MATLAB CODE:

Ib = I2> 0.9627;

4. Image Labeling

· Label the connected components using ‘bwlabel’ function

· Remove components that are smaller in size.

MATLAB CODE:

%Labelling

[Label,total] = bwlabel(Ib,4); % Indexing segments by

% binary label function

%Remove components that is small and tiny

for i=1:total

if(sum(sum(Label==i)) < 500 )

Label(Label==i)=0;

end

5. Find the image properties: Area, Perimeter and Centroid

· Using ‘regionprops’ function, find the Area, Perimeter, Bounding Box and Centroid.

MATLAB CODE:

%Find the properties of the image

Sdata = regionprops(Label,'all');

6. Calculate the Roundness

· Roundness = 4*PI*A/P^2

MATLAB CODE:

%Find the components number

Un=unique(Label);

my_max=0.0;

%Check the Roundness metrics

%Roundness=4*PI*Area/Perimeter.^2

for i=2:numel(Un)

Roundness=(4*pi*Sdata(Un(i)).Area)/Sdata(Un(i)).Perimeter.^2;

my_max=max(my_max,Roundness);

if(Roundness==my_max)

ele=Un(i);

end

7. Find the component with the maximum roundness value

· Find the max of the Roundness value for all the labeled components

8. Show the detected table tennis ball

· Use the ‘BoundingBox’ values to plot rectangle around the ball

· Mark the centroid of the ball

MATLAB CODE:

%Draw the box around the ball

box=Sdata(ele).BoundingBox;

box(1,1:2)=box(1,1:2)-15;

box(1,3:4)=box(1,3)+25;

%Crop the image

C=imcrop(Img,box);

%Find the centroid

cen=Sdata(ele).Centroid;

%Display the image

axes('Position',[0 .1 .74 .8],'xtick',[],'ytick',[])

imshow(Img);

hold on

plot(cen(1,1),cen(1,2),'rx');%Mark the centroid

9. Generate report

· Find the radius using the Equidiameter obtained using ‘regionprops’ function.

· Display the radius,Area,Perimeter and Centroid of the ball.

· Show the Binary and Original image of the cropped ball.

MATLAB CODE:

Rad=(sdata(ele).EquivDiameter)/2;

Rad=strcat('Radius of the Ball :',num2str(Rad));

Area=sdata(ele).Area;

Area=strcat('Area of the ball:',num2str(Area));

Pmt=sdata(ele).Perimeter;

Pmt=strcat('Perimeter of the ball:',num2str(Pmt));

Cen=sdata(ele).Centroid;

Cent=strcat('Centroid:',num2str(Cen(1,1)),',',num2str(Cen(1,2)));

BALL IN MID AIR:

Like "IMAGE PROCESSING" page

Min Filter - MATLAB CODE

MIN FILTER

To find the darkest points in an image.
Finds the minimum value in the area encompassed by the filter.
Reduces the salt noise as a result of the min operation.
The 0^th percentile filter is min filter.

The MIN Filtering is similar to MAX filter. Check MAX filter post to know how the formula is used to filter the pepper noise.

MATLAB CODE:

%READ AN IMAGE

A = imread('board.tif');

A = rgb2gray(A(1:300,1:300,:));

figure,imshow(A),title('ORIGINAL IMAGE');

%PREALLOCATE THE OUTPUT MATRIX

B=zeros(size(A));

%PAD THE MATRIX A WITH ZEROS

modifyA=padarray(A,[1 1]);

x=[1:3]';

y=[1:3]';

for i= 1:size(modifyA,1)-2

for j=1:size(modifyA,2)-2

%VECTORIZED METHOD

window=reshape(modifyA(i+x-1,j+y-1),[],1);

%FIND THE MINIMUM VALUE IN THE SELECTED WINDOW

B(i,j)=min(window);

end

%CONVERT THE OUTPUT MATRIX TO 0-255 RANGE IMAGE TYPE

B=uint8(B);

figure,imshow(B),title('IMAGE AFTER MIN FILTERING');

Like "IMAGE PROCESSING" page

Max Filter - MATLAB CODE

To find the brightest points in an image.
Finds the maximum value in the area encompassed by the filter.
Reduces the pepper noise as a result of the max operation.
The 100^th percentile filter is max filter. Check the 50^th percentile filter i.e the median filter.

MATLAB CODE:

%READ AN IMAGE

A = imread('board.tif');

A = rgb2gray(A(1:300,1:300,:));

figure,imshow(A),title('ORIGINAL IMAGE');

%PREALLOCATE THE OUTPUT MATRIX

B=zeros(size(A));

%PAD THE MATRIX A WITH ZEROS

modifyA=padarray(A,[1 1]);

x=[1:3]';

y=[1:3]';

for i= 1:size(modifyA,1)-2

for j=1:size(modifyA,2)-2

%VECTORIZED METHOD

window=reshape(modifyA(i+x-1,j+y-1),[],1);

%FIND THE MAXIMUM VALUE IN THE SELECTED WINDOW

B(i,j)=max(window);

end

%CONVERT THE OUTPUT MATRIX TO 0-255 RANGE IMAGE TYPE

B=uint8(B);

figure,imshow(B),title('IMAGE AFTER MAX FILTERING');

Like "IMAGE PROCESSING" page

2-D Inverse Discrete Cosine Transform

Consider the result obtained after DCT. (Check 2d-DCT )

Apply Inverse Discrete Cosine Transform to obtain the original Image.

MATLAB CODE:

%2-D INVERSE DISCRETE COSINE TRANSFORM

%PREALLOCATE THE MATRIX

A=zeros(size(B));

Temp=zeros(size(B));

[M N]=size(B);

x=1:M;

x=repmat(x',1,N);

y=repmat(1:N,M,1);

figure,

imshow(log(abs(B)),[]);colormap(jet);title('After DCT');

for i=1:M

for j = 1: N

if(i==1)

AlphaP=sqrt(1/M);

else

AlphaP=sqrt(2/M);

end

if(j==1)

AlphaQ=sqrt(1/N);

else

AlphaQ=sqrt(2/N);

end

cs1=cos((pi*(2*x-1)*(i-1))/(2*M));

cs2=cos((pi*(2*y-1)*(j-1))/(2*N));

Temp=B.*cs1.*cs2*AlphaP*AlphaQ;

A(i,j)=sum(sum(Temp));

end

%OUTPUT

figure,

imshow(abs(A),[0 255]);title('Image after IDCT');

Like "IMAGE PROCESSING" page

2-D Discrete Cosine Transform

DCT is a technique for converting a signal into elementary frequency components.

It is widely used in image compression. Check Inverse discrete cosine transform for the reverse process.

MATLAB CODE:




%CONSIDER A MATRIX

A=[4 2 9 60; 7 10 5 77;88 66 44 3];



%PREALLOCATE THE MATRICES

B=zeros(size(A));

Temp=zeros(size(A));

display(A);



%FIND THE SIZE OF THE
MATRIX

[M N]=size(A);



for i=1:M

    for j=1:N

        

        if(i==1)

          AlphaP=sqrt(1/M);

        else

          AlphaP=sqrt(2/M);

        end

        

        if(j==1)

          AlphaQ=sqrt(1/N);

        else

          AlphaQ=sqrt(2/N);

        end

For A(1,1), m=1 and n=1. If m= 1 then AlphaP=sqrt(1/M)=0.5774

If n=1 then AlphaQ=sqrt(1/N)=0.5000

For A(2,3),m=1 and n=3. AlphaP=sqrt(2/M)=0.8165
AlphaQ = sqrt(2/N) = 0.7071




Temp=0;

       for x=1:M

            for y=1:N

                    cs1=cos((pi*(2*x-1)*(i-1))/(2*M));

                    cs2=cos((pi*(2*y-1)*(j-1))/(2*N));

                    Temp=Temp+(A(x,y)*cs1*cs2);

             end

        end

        B(i,j)=AlphaP*AlphaQ*Temp;

    end

end

%2-D discrete Cosine Transform



display(B);

EXAMPLE 2

%2-D DISCRETE COSINE TRANSFORM FOR AN IMAGE

%READ THE IMAGE

I=imread('coins.png');

I=I(90:150,140:210);

A=double(I);

%PREALLOCATE THE MATRIX

B=zeros(size(A));

Temp=zeros(size(A));

[M N]=size(A);

x=1:M;

x=repmat(x',1,N);

y=repmat(1:N,M,1);

for i=1:M

for j = 1: N

if(i==1)

AlphaP=sqrt(1/M);

else

AlphaP=sqrt(2/M);

end

if(j==1)

AlphaQ=sqrt(1/N);

else

AlphaQ=sqrt(2/N);

end

cs1=cos((pi*(2*x-1)*(i-1))/(2*M));

cs2=cos((pi*(2*y-1)*(j-1))/(2*N));

Temp=A.*cs1.*cs2;

B(i,j)=AlphaP*AlphaQ*sum(sum(Temp));

end

%OUTPUT

figure,

subplot(2,1,1);imshow(I);title('Original Image');

subplot(2,1,2),imshow(log(abs(B)),[]);
colormap(jet);title('After DCT');

Like "IMAGE PROCESSING" page